# Show that the boundary-value problem d / dx (p(x)y') + q(x)y = f (x), 0 x 1, y(0) = , y(1) = , can be transformed by the change of variable z = y x (1

Show that the boundary-value problem

− d / dx (p(x)y') + q(x)y = f (x), 0≤ x ≤ 1, y(0) = α, y(1) = β,

can be transformed by the change of variable

z = y − βx − (1 − x)α

into the form

− d / dx (p(x)z') + q(x)z = F(x), 0≤ x ≤ 1, z(0) = 0, z(1) = 0.

− d / dx (p(x)y') + q(x)y = f (x), 0≤ x ≤ 1, y(0) = α, y(1) = β,

can be transformed by the change of variable

z = y − βx − (1 − x)α

into the form

− d / dx (p(x)z') + q(x)z = F(x), 0≤ x ≤ 1, z(0) = 0, z(1) = 0.

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